Classifying algebraic schemes for musical manifolds

Rok, strany: 2001, 71 - 90

Classification of global musical objects deals with the determination of isomorphism classes in adequate categories of global compositions, the type of objects which play the role of musical manifolds. It relies on two constructions: coefficient systems of affine functions and resolutions of global compositions. These structures are introduced and discussed. As a main result, we derive classifying schemes, and shortly comment on their musical meaning. From the musicological point of view, this is one of the most difficult chapters of mathematical music theory since the relation between classification and musicology, in particular: esthetics, is quite implicit. But classification is a deep concern since it reveals the a priori extent of a structural framework and therefore its power as an expressive tool of artistic activity will be in composition, performance, or understanding.

ISO 690:

Mazzola, G. 2001. Classifying algebraic schemes for musical manifolds. In Tatra Mountains Mathematical Publications, vol. 23, no.3, pp. 71-90. 1210-3195.

APA:

Mazzola, G. (2001). Classifying algebraic schemes for musical manifolds. Tatra Mountains Mathematical Publications, 23(3), 71-90. 1210-3195.